{"id":13833,"date":"2016-01-10T08:34:35","date_gmt":"2016-01-10T08:34:35","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=13833"},"modified":"2016-01-10T08:34:35","modified_gmt":"2016-01-10T08:34:35","slug":"math-definition-of-closed","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-definition-of-closed\/","title":{"rendered":"Math:  definition of closed"},"content":{"rendered":"<h1>The tutor explains the concept of &#8220;closed&#8221; in math.<\/h1>\n<p>If a set is closed under a certain operation, the result you get is still in the set.  For instance, the even numbers are closed under addition:  when you add two even numbers, you get another one.<\/p>\n<p>The odd numbers are not closed under addition:  when you add two odd numbers, you get an even one.<\/p>\n<p>The even numbers are closed under multiplication, but so are the odds.<\/p>\n<p>Source:<\/p>\n<p>Gallian, Joseph A.  <u>Contemporary Abstract Algebra<\/u>, 3rd Ed.  Toronto: D C Heath and<br \/>&nbsp;&nbsp; Company, 1994.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor explains the concept of &#8220;closed&#8221; in math. If a set is closed under a certain operation, the result you get is still in the set. For instance, the even numbers are closed under addition: when you add two &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-definition-of-closed\/\"> <span class=\"screen-reader-text\">Math:  definition of closed<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[1333,1332],"class_list":["post-13833","post","type-post","status-publish","format-standard","hentry","category-math","tag-even-numbers-closed-under-addition","tag-mathematical-definition-of-closed"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13833","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=13833"}],"version-history":[{"count":5,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13833\/revisions"}],"predecessor-version":[{"id":13838,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/13833\/revisions\/13838"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=13833"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=13833"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=13833"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}